PROPOSAL NUMBER.: 0503822 INSTITUTION: University of Washington NSF PROGRAM: STATISTICS PRINCIPAL INVESTIGATOR and Co-PI: Wellner, Jon A PROPOSAL TITLE: Statistical Inverse problems, Semiparametric Models, and Empirical Processes Abstract
Jon A. Wellner will carry out research on statistical inverse problems, semi-parametric models, and on empirical process techniques involved in studying these problems. Wellner and graduate students Marloes Maathuis and Leah Jager will carry out research on competing risks with current status data algorithms and theory for monotone function estimation, and a new family of goodness-of-fit tests related to the Berk-Jones statistic and the associated confidence bands, respectively. The first part of this research will involve further study of nonstandard asymptotics for maximum likelihood and least squares estimators of monotone, multiply monotone and completely monotone functions. The investigator plans to develop new penalized likelihood estimators and new likelihood ratio tests and related confidence intervals, as well as introduce new methods of studying the maximum likelihood estimators themselves. The investigator also intends to refine and improve the existing computational algorithms to the point where additional monte-carlo studies of the various estimators can be carried out for likelihood ratio statistics and profile likelihoods, distribution theory for new limiting distributions, and new distribution theory for point processes. The investigator will investigate new computational algorithms and comparisons of various competing algorithms for several inverse problems.
Basic empirical process tools and methods will be developed and applied to statistical problems concerning semiparametric models and inverse problems. Applications include regression models for panel count data, bivariate interval censored data of several kinds including models for competing risks, regression models for multivariate survival data, and studies of non- and semi-parametric maximum likelihood estimators used in HIV-AIDS research, and two-phase data dependent designs. Wellner also plans to conduct further research on semiparametric models for panel count data with former Ph.D. student Ying Zhang (now at the University of Iowa, Biostatistics) and further work on longitudinal data involving multiple counting processes with former Ph.D. student Hao Liu (now at the University of California at Davis, Biostatistics).
